Stochastic heat equation with infinite dimensional fractional noise: L_{2}-theory | Zendy

Raluca M. Balan | Zendy

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Stochastic heat equation with infinite dimensional fractional noise: L_{2}-theory

Author(s) -

Raluca M. Balan

Publication year - 2009

Publication title -

communications on stochastic analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.224

H-Index - 10

eISSN - 2688-6669

pISSN - 0973-9599

DOI - 10.31390/cosa.3.1.04

Subject(s) - mathematics , sequence (biology) , uniqueness , heat equation , brownian motion , fractional brownian motion , malliavin calculus , stochastic calculus , type (biology) , mathematical analysis , geometric brownian motion , stochastic differential equation , diffusion process , stochastic partial differential equation , partial differential equation , computer science , ecology , knowledge management , statistics , genetics , innovation diffusion , biology

In this article we consider the stochastic heat equation in [0, T ]× Rd, driven by a sequence (β)k of i.i.d. fractional Brownian motions of index H > 1/2 and random multiplication functions (g)k. The stochastic integrals are of Hitsuda-Skorohod type and the solution is interpreted in the weak sense. Using Malliavin calculus techniques, we prove the existence and uniqueness of the solution in a certain space of random processes. Our result is similar to the one obtained in [18] for the stochastic heat equation driven by a sequence (w)k of i.i.d. Brownian motions, in which case the stochastic integrals are interpreted in the Ito sense.

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